6 Continuations (recursive functions) o Program transformation technique based on secondorder functions. New programs are more efficiently represented. o Idea: Given a one-argument function, we find a new two-argument tail-recursive function. The first argument is of the same type that the original one and, the second is a function called continuation. o It is easy to define a new tail-recursive function. o Problem: second-order function representation is expensive. o Benefits when continuations can be represented as simple data structures, for instance, lists. Continuations (recursive functions) o Suppose the following function: f(x) = if p then q else E where x can appear in p, q and E o f appears only one time in E, applied over a sub expression of x, f(s(x)) o In the non trivial case a, where p[a/x] is false, the computation returns r = f(s(a)), γ = λw.ew where Ew = E[f(s(x))/w] o The function γ is applied over r, γ(r)

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